Abstract
Cristobalite, the high-temperature phase of silica, SiO2, stable between 1743 K and the melting point at 1898 K, exists in metastable form at lower temperatures. The cristobalite tetrahedral framework distorts from cubic Fd[unk]m to tetragonal P41212 symmetry at a strongly first order phase transition near 533 K with a latent heat of 1256 Jmol−1. The transition involves a large (5%) volume discontinuity such that single crystals tend to shatter. We measured the thermal evolution of the structural order parameter of the α/β-cristobalite transition and the unit cell strain by neutron time-of-flight and X-ray Guinier powder diffractometry. The system is well described by a single-domain approach with only one active order parameter component, and there is no evidence for a coupling mechanism between the six possible order parameter components. The transition follows a Landau free energy expansion up to sixth order according to [unk] where T0 = 287 K (= Tc – 246 K) and the coefficients αN = 7.44J (mol K)−1, bN = −11.55 kJmol−1, cN = 13.70 kJmol−1 include strain coupling energies and are normalized to give QN(0K) = 1. The fourth order term remains strongly negative after subtraction of the strain-renormalization effects. Our analysis shows that Landau theory may be successfully applied to the quantitative analysis of strongly first order phase transformations, and that the first order character of the α/β-cristobalite inversion is neither strain- nor fluctuation induced. Although the order parameter step ΔQN at the first order discontinuity is as large as 0.8, the thermal expansion of the low temperature phase as well as the strain discontinuity are quantitatively governed by linear coupling of the strain to the square of the order parameter amplitude, corresponding to improper ferroelastic behaviour.
